A194390 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(12) and < > denotes fractional part.

2, 4, 6, 8, 10, 12, 28, 30, 32, 34, 36, 38, 40, 56, 58, 60, 62, 64, 66, 68, 84, 86, 88, 90, 92, 94, 96, 112, 114, 116, 118, 120, 122, 124, 140, 142, 144, 146, 148, 150, 152, 168, 170, 172, 174, 176, 178, 180

Offset

1,1

Comments

Every term is even; see A194368.

Links

Table of n, a(n) for n=1..48.

Mathematica

r = Sqrt[12]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t1, 1]]  (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194390 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194391 *)

Crossrefs

Cf. A010469, A194368, A194391.

Sequence in context: A309716 A198186 A264984 * A187688 A334292 A085884

Adjacent sequences: A194387 A194388 A194389 * A194391 A194392 A194393

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved